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QC 


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George   Da via son 
1825-1911 


STANDARD  MEASURES 


OF 


UNITED  STATES, 
GREAT  BRITAIN,  AND  FRANCE. 


HISTORY   AND   ACTUAL   COMPARISONS. 

WITH 

APPENDIX   OX   INTRODUCTION   OF   THE   MJ&TKE. 


BY 


ARTHUR    S.    C.  /WURTELE, 

ASS'T  ENG.,   N.   Y.    Or^H?  R.    R. 


E.   &  P.   N.    SPON, 

NEW    YORK;    44  MURRAY    STREET. 
LONDON:    16    CHARING    CROSS. 

1882. 


STANDARD   MEASURES 


OF 


UNITED  STATES, 
GREAT  BRITAIN,  AND  FRANCE. 


HISTORY  AND   ACTUAL   COMPAEISONS. 

WITH 

APPENDIX   ON   INTRODUCTION   OF  THE   M^TRE. 


BY 


ARTHUR    S.   C.    WURTELE, 

ASS'T   ENG.,   N.    Y.    C.    &   H.    R.    B. 


E.    &  F.   N.    SPON, 

NEW    YORK;    44  MURRAY    STREET. 

LONDON:    16    CHARING    CROSS. 

1882. 


COPYRIGHT,  1882,  BY  ARTHUR  S.  C.  WURTELE. 


INTRODUCTION. 


DURING  the  preparation  of  this  investigation  of  Stand- 
ard Measures  a  large  number  of  authorities  were  ex- 
amined, including  the  following :  Kelly's  "  Universal 
Cambist,"  Maunder's  "  Weights  and  Measures,"  "  Encyclo- 
paedia Britannica,"  "  Chambers'  Encyclopaedia,"  Williams' 
"  Geodesy,"  Hymer's  works,  "  Smithsonian  Reports,"  "  Coast 
Survey  Reports,"  Herschel's  "  Astronomy,"  etc.  The  only 
concise  and  clear  statement  I  found  was  J.  E.  Hilgard's 
report  to  the  Coast  Survey  on  standards  in  1876,  which  I 
was  gratified  to  find  coincides  with  my  deductions. 

ARTHUR  S.  C.  WURTELE. 
ALBANY,  November  26,  1881. 


20779 


STANDARD    MEASURES, 


A  STANDARD  measure  of  length  at  first  sight  appears  to 
be  very  simple — merely  a  bar  of  metal  of  any  length,  ac- 
cording to  the  unit  of  any  country ;  and  comparisons  of 
different  standards  do  not  seem  to  present  any  difficulty. 
But  on  looking  further  into  the  thing,  we  find  that  stand- 
ards are  referred  to  some  natural  invariable  length,  and 
we  are  at  once  confronted  with  a  mass  of  scientific  reduc- 
tions giving  different  values  to  the  same  thing,  according 
to  successively  improved  means  of  observation.  We  find, 
also,  that  comparisons  of  one  standard  with  another  differ, 
as  given  by  reductions  carried  to  great  apparent  exactness. 
1  Every  author  appears  to  assume  the  right  of  using  his 
own  judgment  as  to  what  reduction  is  to  be  considered 
the  most  exact,  and  the  result  is  a  very  confusing  differ- 
ence in  apparently  exact  figures,  with  nothing  to  show 
how  these  differences  arise. 

I  have  endeavored  to  indicate  what  may  be  the  cause 
of  this  confusion  by  giving  the  figures  of  actually  ob- 
served comparisons  and  reductions;  in  a  manner,  the  roots 
of  the  figures  used  as  statements  of  length. 

Sir  Joseph  Whitworth  gives  ^-QU-  of  an  inch  as  the 
smallest  length  that  can  be  measured  with  certainty,  with 
an  ultimate  possibility  of  YOOOOOO  of  an  inch  ;  but  imper- 
ceptible variations  of  temperature  affect  these  infmitesi- 


rnal  lengths  to  such  an  extent  that  he  believes  the  limit 
can  only  be  reached  at  a  standard  temperature  of  85°  F. 
to  avoid  the  effect  of  heat  of  the  body. 

It  appears  to  me  that  comparisons  should  be  made  of 
double  yards  and  metres  with  the  old  French  toise,  as  the 
limit  of  exactness  would  be  thereby  doubled. 

Another  great  defect  in  statements  of  relative  values  is 
the  omission  of  necessary  facts — the  material  of  which 
the  bars  or  standards  are  made,  the  temperature  at  which 
comparison  was  made,  and  the  standard  temperatures  used 
as  to  the  final  reduction,  with  the  coefficient  of  expansion 
adopted. 

Again,  bars  of  different  metals  appear  in  time  to  sensi- 
bly change  their  relative  length. 

ENGLISH   STANDARDS   OF  LENGTH. 

The  first  establishment  of  a  uniform  standard  appears 
to  have  been  made  in  1101  by  Henry  I,  who  is  said  to 
have  fixed  the  ulna  (now  the  yard)  at  the  length  of  his 
arm;  but  nothing  definite  was  done  till  1736,  when  the 
Royal  Society  took  steps  toward  securing  a  general  stand- 
ard, and  in  1742  they  had  a  standard  yard  made  by 
Graham  from  a  comparison  of  various  yards  and  ells  of 
Henry  VII.  and  Elizabeth,  that  were  kept  in  the  Ex- 
chequer. 

Two  copies  of  the  Eoyal  Society  standard  yard  were 
made  by  Bird  in  1758  for  a  committee  of  Parliament,  one 
of  which  was  marked  "standard  of  1758,"  and  the  other 
1760.  But  no  exact  legal  standard  was  yet  established, 
as  shown  by  comparisons  in  1802  of  the  various  standard 
measures  in  use  which  Pictet,  of  Geneva,  made  with  an 
accurate  scale  by  Troughton,  using  means  exact  to  the 
ten  thousandth  part  of  an  inch,  with  the  following  results 
at  the  temperature  of  62°  F. : 


Troughton  Scale 36.00000  inches. 

Parliamentary  Standard  (1758,  Bird) 36.00023  " 

Royal  Society                    (1760,     "  ) 35.99955  " 

(Graham) 36.00130  " 

Exchequer              "          , 35.99330  " 

Tower                     "            36.00400  " 

Gen.  Roy                "          (Trig.  Survey)  ..  .36.00036  " 

Parliament  finally  undertook  to  reform  the  measures  of 
England,  and  appointed  a  commission  in  1818,  under 
whose  authority  Capt.  Kater  compared  the  standard  yards 
then  in  use  with  the  following  results,  as  referred  to  the 
Indian  Survey  standard : 

Col.  Lambton  Standard  (Indian  Survey)  .  .36.000000  inches. 

Bird's  Standard  (1760) 36.000059      " 

Sir  Geo.  Schuckburgh's  Standard 36. 000642      " 

Ramsden's  Bar.  Ordnance  Survey 36.003147      " 

Gen.  Roy's  Scale 36.001537      " 

Royal  Society  Standard 36.002007      " 

The  commission  reported  in  favor  of  adopting  Bird's 
standard  of  1760,  as  it  differed  so  slightly  from  Sir  George 
Schuckburglrs  standard  (wrhich  had  been  used  in  deduc- 
ing the  value  of  the  French  metre)  that  those  values  could 
be  assumed  as  correct.  They  also  established  the  length 
of  the  seconds  pendulum  at  level  of  sea  in  London  and  in 
vacuo  as  39.13929  inches.  The  seconds  pendulum  had 
been  previously  fixed  by  Wollaston  and  Play  fair  in  1814 
as  39.13047  inches. 

On  this  report,  an  Act  of  Parliament  in  1823  declared 
the  only  standard  measure  of  length  for  the  United  King- 
dom to  be  the  yard  as  given  by  the  distance  at  32°  F. 
between  two  points  in  gold  studs  on  the  brass  bar,  made 
by  Bird,  and  marked  "Standard  of  1760,"  and  in  the 
keeping  of  the  Clerk  of  the  House  of  Commons;  also  it 
referred  this  standard  yard  to  the  natural  standard  of  a 
pendulum  vibrating  seconds  of  mean  solar  time  at  the 


level  of  the  sea,  in  vacuo  at  London  and  temperature  of  32° 
F.,  as  in  the  proportion  of  36  to  39.13929  ;  so  that  a  pen- 
dulum 36  inches  long  ought  to  make  90088.42  vibrations 
in  24  hours. 

The  Royal  Society  had  a  copy  of  the  legal  standard 
made  by  Bailey  in  1834 ;  and  in  the  same  year  the  Par- 
liamentary standard  was  destroyed  by  fire  at  the  burning 
of  the  Houses  of  Parliament,  leaving  the  kingdom  again 
without  a  legal  standard. 

All  attempts  made  by  a  commission  consisting  of  Airy, 
Bailey,  Herschel,  Lubbock,  and  Sheepshanks,  to  restore  the 
standard  by  means  of  the  seconds  pendulum  failed  in 
exactness,  on  account  of  the  many  conditions  of  a  vibrating 
pendulum,  and  recourse  was  had  to  the  Royal  Society 
standard,  which  had  been  carefully  compared  by  Captain 
Katerin  1818,  and  from  this  in  1838  Bailey  and  Sheepshanks 
made  six  bronze  bars,  one  inch  square,  and  38  inches 
long,  which  in  1855  were  legalized  by  Act  of  Parliament, 
and  the  English  standard  of  length  defined  as  follows : 

"That  the  straight  line  on  distance  between  the  centres 
of  the  transverse  lines  in  the  two  gold  plugs  on  the 
bronze  bar  deposited  in  the  Exchequer  shall  be  the 
genuine  standard  yard  at  the  temperature  of  62°  Fahrenheit ; 
and  if  lost,  it  shall  be  replaced  by  means  of  its  copies." 

The  French  metrical  system  was  made  legal  permissively 
in  1864,  at  the  length  established  by  Captain  Kater,  re- 
ferred to  in  Act  of  Parliament  of  1823,  of  1  metre  equal  to 
39.37079  inches,  or  3.28089916  feet. 

These  are  the  standards  now  in  use  in  the  United 
Kingdom. 

UNITED  STATES. 

By  the  Constitution  of  the  United  States  Congress  is 
charged  with  fixing  the  standard  of  measures  (Art.  1, 


sec.  8)  ;  but  as  no  enactment  has  been  made  by  Congress, 
the  standard  yard  in  England,  which  was  legal  previous  to 
1776  in  the  Colonies,  is  the  standard  yard  of  the  United 
States,  and  does  not  differ  with  the  English  standard 
yard. 

Under  resolution  of  Congress  in  1 830,  Mr.  Hassler  was 
employed  to  examine  the  standards  in  use. 

Considerable  discrepancies  were  found,  but  the  mean  of 
all  examined  corresponded  very  nearly  with  the  English 
standard,  and  in  1832  the  recommendation  of  Mr.  Hassler 
was  adopted,  and  the  standard  yard  defined  as  the 
distance  between  the  27th  and  63d  inch  marks,  at  the 
temperature  of  62°  F.,  on  the  brass  scale  82  inches  long, 
being  an  exact  copy  of  Sir  George  Schuckburgh's  standard, 
made  by  Troughton,  of  London,  for  the  Coast  Survey,  and 
deposited  in  the  Office  of  Weights  and  Measures  at  Wash- 
ington. 

In  1836  an  Act  of  Congress  ordered  standards  to  be 
sent  to  each  Governor  of  a  State,  and  the  work  was  done 
under  direction  of  Mr.  Hassler. 

In  1856,  two  copies  of  the  English  standard  yard,  as 
restored  after  destruction  of  the  original  standard  by  fire 
in  1834,  No.  11  of  bronze,  and  No.  57  of  Low  Moor  wrought 
iron,  were  presented  to  the  United  States  by  Airy. 

The  United  States  Troughton  standard  bar  being  com- 
pared with  No.  11  was  found  to  be  longer  by  0.00085 
inch,  or  in  proportion  of  1  to  1.0000237216,  about 
l£  inches  in  a  mile,  according  to  Report  of  Secretary  of 
Treasury  in  1857. 

Later  comparisons  made  by  J.  E.  Hilgard,  of  the  Coast 
Survey,  at  the  British  Standards  Office,  between  No.  11  and 
the  standard  imperial  yard,  give  No.  11  as  0.000088  inch 
shorter,  or  it  would  be  of  standard  length  at  temperature 
of  62.25°  F. 


We  may  infer  that  the  Troughton  standard  is  too  long 
by  0.000762  inch,  or  would  be  standard  length  at  tem- 
perature 59.77°  F.  instead  of  at  62°  by  making  expansion 
reduction  with  Airy's  coefficient  for  the  bronze  of  the 
imperial  standards,  0.000342  inch  per  yard  for  1°  F. 

The  metre  was  made  a  legal  standard  permissively  in 
1866  ;  the  United  States  metre  standard  being  one  of  the 
12  iron  metre  bars  made  and  verified  for  the  French  Gov- 
ernment in  1799  on  the  adoption  of  the  metrical  system, 
and  brought  to  America  by  Mr.  Hassler  in  1800,  the 
relative  value  being  fixed  by  Act  of  Congress  at  39.37 
inches. 

The  relative  value  of  39.36850154  United  States  inches, 
as  obtained  by  Mr.  Hassler,  corrected  to  62°  F.,  was  used 
by  the  Coast  Survey  till  1868,  when  it  was  found  advisable 
to  use  the  relative  value  of  39.3704  as  deduced  by  Clarke. 
Since  1800  several  standard  metre  bars  were  sent  to  the 
United  States  by  the  French  Government,  and  on  com- 
parison, there  appearing  to  be  a  slight  discrepancy,  the 
original  iron  standard  metre  bar  was  sent  to  Dr.  F.  A.  P. 
Barnard  in  Paris,  and  in  1867  it  was  compared  with  the 
French  platinum  standard,  which  is  only  used  once  in  ten 
years  to  verify  other  standards. 

A  difference  was  found  by  this  comparison  of  only 
.00017  millimetre  or  Y6TTo~oo~  incn>  which  being  only  y^of 
an  inch  in  a  mile  is  inappreciable. 

FRANCE. 

The  standard  of  length  of  the  systenie  ancient  was  the 
toise  of  6  pieds,  divided  into  12  pouces  of  12  lignes 
each. 

The  origin  of  the  toise  is  not  known,  but  it  was  probably 
legally  established  by  Philip  Le  Bel,  about  1300,  as  he 
first  appears  to  have  taken  steps  toward  a  uniform  sys- 


tern  of  measures  in  France.  In  the  13th  century  the 
toise  is  mentioned  by  Ch.  Le  Rains.  In  the  14th  century 
Menongier  writes  that,  in  marching,  the  sight  should  strike 
the  ground  4  toises  in  front.  In  the  fifteenth  century  Pere- 
forest  brings  in  the  toise,  and  in  the  sixteenth  century  the 
Contume  de  Berry  says.  "  We  use  in  this  country  two  toises  ; 
one  for  carpenters  of  5  pieds  and  a  half,  the  other  for  ma- 
sons of  6  pieds." 

Picard  used  the  toise  in  his  measurement  of  an  arc  of 
meridian  from  Malvoisin  to  London  in  1669. 

The  meridians  measured  by  the  Academy  in  1735  to  settle 
the  question  of  the  figure  of  the  earth  were  made  by  means 
of  two  standard  toises,  known  as  the  "  Toise  du  Nord,"  and 
the  "  Toise  du  Sud." 

The  first,  used  by  Maupertuis,  Clairanlt,  and  Le  Monnier, 
in  Lapland,  was  destroyed  by  immersion  in  sea-water, 
when  their  ship  was  wrecked  on  the  return  voyage. 

The  second,  with  which  La  Condamine,  Bourgner,  and 
Godin  operated  in  Peru,  was  the  original  of  the  toise  Cani- 
vet  made  in  1768,  and  of  the  standards  used  in  determining 
the  metre. 

The  commencement  of  the  move  for  a  scientific  standard 
of  length  in  France  which  resulted  in  the  m&tre  was  in 
1790,  when  the  revolutionary  government  proposed  to 
England  the  formation  of  a  commission  of  equal  numbers 
from  the  English  Royal  Society  and  the  French  Academy, 
for  the  purpose  of  fixing  the  length  of  the  seconds  pendu- 
lum at  latitude  45°  as  the  basis  of  a  new  system  of  meas- 
ures. This  proposal  was  not  favorably  received,  and  the 
Academy,  at  the  request  of  government,  appointed  as  a 
commission  Borda,  Lagrange,  Laplace,  Monge,  and  Condor- 
cet,  to  decide  whether  the  seconds  pendulum,  the  quarter 
of  the  equator,  or  the  quarter  of  a  meridian,  should  be  used 
as  the  natural  standard  for  the  new  system  of  measures. 


10 

They  settled  on  the  last  as  best  for  the  purpose,  and  resolved 
that  the  ten  millionth  of  the  meridian  quadrant,  or  distance 
from  equator  to  pole,  measured  at  sea  level,  be  taken  for 
basis  of  the  new  system,  and  be  called  a  metre. 

Delambre  and  Mechin  were  at  once  charged  with  re- 
measurement  of  the  meridian  surveyed  in  1739  by  La  Caille 
and  Cassini,  from  Dunkirk  to  Perpignan,  and  its  ex- 
tension to  Barcelona. 

Operations  were  commenced  in  1792,  and  carried  on 
with  great  accuracy  to  completion  in  1799;  Delambre 
working  between  Dunkirk  and  Paris,  and  Mechin  between 
Paris  and  Barcelona. 

The  distance  measured  from  Dunkirk  to  Barcelona  was 
9°  40'  24.24"  of  arc,  or  1,075,059  metres,  as  reduced  to  the 
new  standard. 

The  "  toise  de  Peru"  was  the  standard  used  in  the  work 
at  a  temperature  of  13°  E. 

Two  base-lines  were  measured  with  Borda's  compensat- 
ing bars  of  brass  and  platinum ;  one  at  Melun,  near  Paris, 
6076  toises  long,  and  the  second  at  Perpignan,  6028  toises 
long,  and  though  over  900,000  metres'  apart,  the  calculated 
length  differed  by  only  10  pouces. 

This  meridian  was  afterward,  in  1806,  extended  by 
Gen.  Boy  to  Greenwich,  on  the  north,  and  by  Biot  and 
Arago  to  Formentera,  on  the  south.  The  results,  as  given 
by  Laplace  in  centesimal  degrees  and  metres,  are  as 
follows  : 

Greenwich 57.19753°  .0  metres. 

Pantheon,  Paris 54.27431°        292,719.3       " 

Formentera 42.96178°     1,423,636.1       " 

The  middle  of  the  arc  being  50.079655°  Cent.,  or  45°  4' 
18.0822"  Sexa.,  and  the  middle  degree  centesimal  being 
veiy  nearly  100,000  metres. 


11 

The  determination  of  the  final  result  of  these  geodetic 
measurements  was  referred  to  a  committee  of  20  members; 
9  named  by  the  French  Government,  and  the  others  by  the 
governments  of  Holland,  Savoy,  Denmark,  Spain,  Tuscany, 
and  of  the  Cisalpine,  Ligurian,  and  Swiss  republics,  on  the 
invitation  of  France. 

This  committee  established  the  meridian  quadrant  at 
5,130,740  toises ;  making  the  metre  0.513074  of  the  toise, 
or  36.9413  pouces,  or  443.296  lignes,  and  the  toise 
1.94903659  metres. 

Iron  standard  metre  bars,  12  in  number  were  made  by 
Borda,  also  2  of  platinum  and  4  standard  toise  bars. 

The  12  standard  iron  metre  bars  were  sent  to  different 
countries,  after  being  verified  by  the  French  Government, 
and  on  the  2d  of  November,  1801,  the  metrical  systeme 
was  legalized  by  France,  and  the  standard  unit  of  length 
declared  to  be  the  ten  millionth  part  of  a  meridian  quad- 
rant of  the  earth,  as  defined  by  the  distance  at  a  tem- 
perature of  0°  Centigrade  (32°  F.)  between  two  points  on  a 
platinum  bar  in  the  keeping  of  the  Academy  of  Science 
at  Paris.  This  standard  bar  is  used  only  once  every  ten 
years  for  exact  comparisons,  as  stated  by  Dr.  F.  A.  P. 
Barnard. 

About  1837  Bessel,  by  a  combination  of  11  measured 
arcs  of  meridian,  deduced  the  quadrant  of  meridian  as 
5,131,179.81  toises  instead  of  5,130,740  toises,  as  fixed  by 
law.  This  would  make  to  quadrant  10,000,565.278  legal 
metres,  or  would  increase  the  metre  length  from  443.296 
lignes  to  443.334  lignes,  agreeing  very  nearly  with 
result  obtained  by  Airy  in  1830,  from  a  combination  of 
13  measured  arcs. 

The  following  are  the  measured  arcs  used  by  Bessel  and 
Airy  ;  the  combinations  being  indicated  by  initial  letters, 
A  and  B. 


12 


CO 


CD  ^J"1 

Oi  O 
rH  CO 


Oi  O  00 


CO  i>  O  O  i> 


1Q 


i>  rH 


CO  i>  CO  CO  O  <M 
iO  1O  rH  G<*     rH 


Q  CD  CO  t-  Th  rH 

rH  CO  CO 


IO 


i>  t>  1O 

CO  iO  CO 

o   o  o 

rH  O  CO 


G^J  O  rH  O  £*•  O  O  G^ 

CO    CO  iO   *O    G»    G> 

OQOOOOOO 

GOrHrHG>iCOGMGOG> 


CiGOt>Tt<t>COT^t^ 
(M   iO    CO  rH    CO 


^ 


•     0) 

•    +. 

:    - 

3                ^ 

:  «!  r 

8       •       •       • 

'•  2  93    :  i 

^            rH              f 

>               C 

.  —  Svanberg,  Sweden  
.  —  Maupertuis,  Sweden..  .. 

RfvilTTO  T?TK2C!ia 

%    o 

P      r 

I] 

ill 

>      <D    r- 
"       >      C 

Hi 

i  &  p 

.  —  Schumacher,  Denmark  .  . 
.—Ganss,  Hanover  

.  —  Roy  and  Kater,  England. 

a  n  a 

.  —  Lacaille  and  Cassini,  Frai 
.  —  Delambre  and  Mechin,  Fi 
.  —  Boscovich,  Rome  

.  —  Lambton,  India  .  ....... 
.  —  Lambton  and  Everest,  In 
.  —  Lacondamine,  Peru  

T,Q/^Qillo  r^QT-v£i  C^-r\r\f\  TTr\T-i/: 

r    a 

1     5 

r  •! 

5           o 

'-  I 

r.l 

>    T 

J   §    a 

13 

The  following  different  lengths  of  the  metre  have  been 
obtained  : 

As  adopted  by  France,  1801 443.296      lignes. 

According  to  Delambre 443.264  " 

"          Bessel 443.33394    .  " 

Airy 443.32387       " 

"          Clarke 443.36146 

From  Peru  Meridian 443. 440  " 

The  length  of  a  pendulum  vibrating  100,000  times  in  a 
mean  solar  day  was  determined  in  numerous  careful  ex- 
periments by  Biot,  Arago,  and  Mathieu,  in  metres  of 
443.296  lignes,  as  follows : 

Dunkirk 56.671at.  Cent. .    0  above  sea.  .0.7419076  metres. 

Paris 54.26        "       ..65         "       ..0.7418870       " 

"     by  Borda. 54.26        "       ..0         "       ..0.7416274       " 

Bordeau 49.82        "       ..0         "       ..0.7412615       " 

Formentera..  .42.96        "       ..196         "       ..0.7412061 

Borda  also  determined  the  length  of  the  seconds 
pendulum  at  Paris,  in  vacuo : 

First  result 440.5595  lignes=0.9938267  metre. 

Second  result "  "     =0.9938460     " 

As  given  by  Ganot "  "     =0.9935  " 

In  1812  the  systeme  usuelle  was  established,  of  which 
the  unit  was  one  third  of  the  metre,  with  the  old  name  of 
pied,  and  duodecimally  divided  into  pouces  and  lignes. 

This  system  continued  in  use  till  1840,  when  it  was 
abolished  by  law,  and  the  names  of  pied,  pouce,  and  ligne 
forbidden  under  penalties.  So  the  metre,  decimally  di- 
vided, remains  the  only  legal  measure  of  length  in  France. 

COMPARISONS   OF  UNITED    STATES  AND 
ENGLISH  STANDARDS. 

In  1832,  under  resolution  of  Congress,  Mr.  Hassler 
compared  the  different  standard  yards  in  America,  with 


14  * 

the  following  results,  using  the  yard  between  the  twenty 
seventh  and  sixty-third  inches  on  the  scale  made  of  bronze 
by  Troughton,  of  London,  for  the  United  States  Coast 
Survey,  as  the  reference,  that  being  identical  with  Sir 
George  Schuckburg's  standard : 

Troughton  Scale,  mid.  yard 36.0000000  inches. 

"  "      between  platinum  points.  ..35.9989758      " 

Jones  yard  in  State  Department 35.9990285      " 

Iron  yard  in  Engineer  Department 35.9987760      " 

Brass  yard,  Albany,  Sec.  of  State 36.0002465      " 

Gilbert  yard,  University  of  Virginia 35.9952318      " 

In  1856  the  Troughton  standard  bronze  scale  was 
compared  with  the  bronze  standard  yard  No.  11,  which 
was  sent  over  by  Airy  as  a  copy  of  the  English  im- 
perial standard,  as  restored  after  destruction  of  the  origi- 
nal standard  by  fire  in  1834,  and  the  United  States 
standard  was  found  to  be  longer  by  0.00085  inch. 

Later  comparisons  by  J.  E.  Hilgard,  of  the  Coast  Sur- 
vey, of  the  bronze  standard  No.  11  with  the  imperial 
standard  yard,  at  the  British  Standards  Office,  gave  No. 
1 1  as  0.000088  shorter  than  the  imperial  standard. 

Hassler's  reduction  of  the  metre,  as  deduced  by  Beach 
at  62°  F.,  39.36850154,  compared  with  the  English  reduc- 
tion of  the  metre,  39.37079  inches,  gives  an  excess  to  the 
United  States  Standard  of  0.002029  inch. 

The  following  reductions  have  been  given  for  the 
United  States  yard  in  English  inches : 

Report  of  Sec.  of  Treas.,  1857 36.00087  =  1.00002416 

Chambers'  Encyclopaedia,  1872. . .  .35.00087 

xu_     s~       "  "  "    ....36.0020892  =1.0000580334 

£^£/  Trautwine 36.0020894  =  1.000058038 

'  \JVlathewson,  U.  S.  surveyor 36.00208944  =  1.00005804 

Hassler  and  Beach 36.002092  =  1.00005811 

J.  E.  Hilgard,  Coast  Survey 36.00076  =  1.000021 


15 

To  Mr.  Hassler's  reduction  the  name  of  United  States 
inch  has  been  applied  ;  but  his  reduction  is  not  correct,  as 
he  used  a  rate  of  expansion  for  brass  deduced  by  himself 
of  0.0003783  inch  in  one  yard  for  1°  F.,  and  later  experi- 
ments show  that  the  smaller  rate  of  0.000342,  deduced  by 
Airy,  is  more  correct. 

By  correcting  Hassler's  reduction  with  the  later  rate  of 
expansion,  J.  E.  Hilgard  shows  that  the  difference  would 
be  very  small,  or  only  36.0002286  =  1.00000635,  or  about 
f-  of  an  inch  in  a  mile. 

In  Coast  Survey  report  for  1876,  J.  E.  Hilgard  calls  at- 
tention to  another  difficulty  in  the  matter  of  extreme 
accuracy,  in  the  uncertainty  with  regard  to  the 
permanence  in  the  length  of  a  bar,  and  states  that 
the  bronze  standard  bar  No.  11  and  the  Low  Moor  iron 
standard  bar  No.  57,  presented  to  the  United  States  by 
Great  Britain,  are  found  to  have  changed  their  relative 
length  by  0.00025  inch  in  25  years ;  the  bronze  bar  being 
now  relatively  shorter  by  that  amount.  This  subject,  he 
states,  is  undergoing  further  investigation. 

COMPAKISON  OF  UNITED  STATES  AND 
FRENCH  STANDARDS. 

In  1817  Mr.  Hassler  examined  the  French  standards  in 
America,  for  the  Coast  survey,  using  the  Troughton  bronze 
standard  scale,  which  is  identical  with  Sir  George  Schuck- 
burg's  standard,  as  the  reference,  with  the  following  results, 
all  being  reduced  to  temperature  of  32°  F. 

Original  Iron  Metre,  1799 39.381022708  inches. 

Lenoir  Iron  Metre,  Coast  Survey 39.37972015 

"       Brass     "  "  39.380247972      " 

"      Eng.  Dept 39.38052739 

Canivet  Iron  Toise,  1768 76.74334472 

Lenoir     "         "  76.74192710 


16 

In  1814  Trough  ton  had  compared  with  his  own  scale  in 
London  two  of  the  above. 

Lenoir  Iron  Metre,  C.  S 39.3802506    inches.. 

"      Brass     "       "     39.3803333 

In  1832,  under  resolution  of  Congress,  Hassler  again 
compared  the  French  standards  in  the  United  States,  using 
as  before  the  Trough  ton  scale,  and  reducing  all  to  tem- 
perature of  32°  F.  as  follows  : 

Original  Iron  Metre,  1799 39.3808643    inches. 

Lenoir  "  "     C.  S 39.3799120 

Brass  Metre  C.  S 39.380447 

Eng.  Dept 39.3801714 

"        in  1829  39.3807095 

Fortin  "          State  Dept 39.3796084 

Treas.  "     39.3795983 

Iron  Metre       "        "     39.3807827 

Gilbert  "  Univ.  of  Virg 39.365408          " 

Platinum  Metre 39.3803278 

"  (Nicollet) 39.380511 

Canivet  Iron  Toise,  1768 76. 74290511      " 

Lenoir  "         1799 76.74047599      " 

From  the  mean  of  his  comparisons  between  the  United 
States  brass  Troughton  standard  yard  and  the  authentic 
French  standard  metres  used  by  the  Coast  Survey,  Hassler, 
in  1832,  deduced  the  value  of  the  metre  at  39.3809172 
inches,  at  32°  F.,  and  by  correction  for  expansion  to 
United  States  standard  temperature  of  62°  F.,  he  made 
the  metre  at  32°  equal  to  39.36850154  inches  at  62°  F. 

The  British  imperial  standard  and  the  United  States 
Troughton  standard  differ  by  only  0.000762  inch,  which 
applied  to  the  English  reduction  of  39.37079,  would  give 
39.36996  as  the  relative  value  according  to  Troughton 
standard. 


17 

The  difference  between  these  reductions  is  probably  to 
be  attributed  to  the  use  of  different  rates  of  expansion, 
in  correcting  for  standard  temperatures,  which  vary  con- 
siderably, according  to  high  authority  as  follows  for  brass 
atl°F. 

Whitworth,  1876. . . .  0.00000956    =  0.00034416  in.  per  yard. 

Borda,  1799 0.000009913  =  0.00035687  « 

Smeaton,  1750. .....  0.000010417  =  0.00037501 

Hassler 0.000010508  =  0.0003783  " 

Eamsden,  1760 0.000010516  =  0.0003786 

Faraday,   1830 0.00001059    =  0.00038124 

And  for  the  bronze  of  which  the  British  imperial  stand- 
ards are  made : 

Airy  and  Sheepshanks. . .     0.0000095    =  0.000342  in.  per  yard. 
Fizeau 0.00000975-=  0.000351  " 

The  correction  at  Ramsden's  rate  is  nearly  identical  with 
Hassler's,  and  gives  39.3684933 ;  at  Whitworth's  rate  it 
would  give  39.36962,  very  nearly  the  same  as  deduced 
from  the  difference  between  the  British  Imperial  standard 
and  the  United  States  Troughton  standard.  The  results  of 
Sir  Joseph  Whitworth  were  obtained  by  use  of  all  late 
improvements  for  scientific  precision,  and  they  must  be 
accepted  as  most  reliable. 

It  would  appear  preferable  to  give  comparisons  at  the 
same  temperature  in  connection  with  the  corrected  result, 
so  that  international  comparisons  of  scientific  measurements 
may  not  be  vitiated  by  accidental  variations. 

COMPARISON  OF  ENGLISH  AND  FRENCH 
STANDARDS. 

When  the  metre  standard  was  established  in  France' 
1799,  it  was  compared  with  Sir  George  Schuckburg's 


18 

standard  yard  by  Captain  Kater.  The  quadrant  of 
10,000,000  metres,  or  5,130,740  toises,  was  determined  to  be 
32,808,992  English  feet,  giving  the  metre  equal  to 
3.2808992  English  feet,  or  39.37079  inches,  and  the  toise 
equal  to  6.3945925921  English  feet. 

In  1814  Wollaston  and  Playfair,  by  comparison  with  the 
platinum  metre  standard  at  55°  F.,  deduced  the  metre  as 
equal  to  39.3828  English  inches/ 

During  the  geodetic  operations  of  General  Roy  in  1802, 
who  used  60°  F.  as  standard  temperature,  Pictet's  compari- 
sons, using  means  capable  of  measuring  the  10,000th  part 
of  an  inch,  gave  the  metre  standard,  which  is  used  at  32°  F. 
as  standard  temperature,  at  39.3828  English  inches  ;  this 
corrected  for  temperature  by  Dr.  Young,  gave  3  .371  English 
inches  at  62°  F.;  which  result  was  confirmed  by  Bird,  Mas- 
kelyne  and  Laudale. 

In  1823,  by  Act  of  Parliament  on  report  of  committee, 
the  metre  is  fixed  as  39.37079  English  inches. 

In  1800  the  Royal  Society,  by  comparison  with  two  toise 
standards  sent  by  Lalande  to  Maskelyne,  deduced  the 
metre  as  39.3702  English  inches. 

Later  comparisons  by  Clarke  in  the  Ordnance  Survey 
Office  at  Southampton,  in  1866,  give  the  metre  as  39.37043 
inches. 

The  French  Academy  of  Sciences  by  comparison  with 
Sir  George  Schuckburg's  standard  at  temperature  of  32°  F., 
deduced  the  metre  as  39.3824  English  inches,  which  reduced 
to  standard  temperature  of  62°  F.,  would  be  39.3711,  or 
slightly  in  excess  of  the  value  deduced  by  Dr.  Young  from 
Pictet's  comparisons. 

The  legal  value  in  England  is  one  metre  equal  to 
39.37079,  and  the  latest  reduction  is  39.37043  inches  by 
Clarke  in  1866,  which  is  probably  the  most  exact  re- 
duction. 


19 

DIFFERENT  REDUCTIONS  OF  THE  FRENCH  TOISE  INTO 
ENGLISH  FEET. 

Captain  Kater,  1799 6.3945925921  feet. 

Hassler,  1832 6.3951409 

Chambers' Encyclopaedia 6.39456 

Mathematics 6.394662 

Wallace 6.39462 

Nystrom 6.39625 

Alexander 6.39435 

Dana..  6.3946 


The  following  table  of  reductions  as  used  shows  clearly 
how  great  a  confusion  exists  in  the  matter  of  comparisons  : 


MfiTRE   IN  INCHES. 

Phcenixville  Hand-book 39.368          inches. 

Hassler 39.36850154     " 

.39.370788 

"       39.3809172       " 

Trautwine 39.368505 

39.37079 

Silliman 39.368505 

«        39.37079 

Chambers'  Encyclopedia 39.36850535     " 

«  "  39.3707904       " 

Act  of  United  States  Congress,  1866 39.37  " 

Smithsonian  Report • 39.37  " 

Youmans 39.37 

Davies '..3937 

Homan's  Encyclopaedia 39.37008 

Weale ". 39.3702 

Ordnance  Survey  (England,  1866) 39.37043 

Clerk  Maxwell 39.37043 

Capt.  Clarke 39.3704316       " 

J.  M.  Rankine  (1870) 39.3704316       " 

(1866) 39.3707904       " 

Alexander  (weights  and  measures) 39.37068 

Ganot 39.370788 

Vose  .  ..39.370788 


20 

Act  of  British  Parliament,  1823 39.37079      inches. 

Encyclopaedia  Britannica 39.37079 

Hymer 39.37079 

Davies  and  Peck 39.37079 

J.  W.  Clarke 39.37079 

Dana 39.37079  " 

Whittaker 39.37079 

Sommerville 39.3707904       " 

Chambers'  Mathematics 39.3707904       " 

Gwilt's  Encyclopaedia 39.3707904       " 

Gillespie 39.3707904       " 

Capt.  Kater 39.3708 

Appleton's  Encyclopaedia 39.37079 

Van  Nostrand 39.3708 

D'Aubuisson 39.3708 

Johnson  (draftsman) 39.3708 

Encyclopaedia  Americana 39.371 

Jameson's  Dictionary 39.371 

Herbert's  Encyclopaedia 39.371 

Popular  "  39.371 

Molesworth 39.371 

Dr.  Young  (1802) 39.371 

Wallace  (engineer) 39.371 

Nystrom 39.38091 

Hencke 39.3809172       " 

Act  of  Canadian  Parliament,  1873. .  ....  .39.3819 

Paris  Academy 39.3824  " 

LENGTH  OF  THE   SECONDS   PENDULUM  AS   GIVEN   BY 
DIFFERENT  WRITERS. 

NEW  YOKK.— Hencke 39.1012  inches. 

Bartlet 39.11256  " 

Nystrom 39.1017 

Ganot 39.1012 

Byrne 39.10153  " 

Wallace 39.10153  " 

LONDON. — Hencke 39.13908  " 

Gillespie 39.13929  " 

Chambers'  Encyclopaedia 39.13929  " 

Williams'  Geodesy 39.13929  " 


21 

LONDON.— Act  of  Parliament,  1823 39.13929  inches. 

Wallace  (engineer) 39.1393        " 

Chambers'  Mathematics 39.1393 

Hymer  Astronomy 39.13734      " 

Bartlet 39.13908      " 

Vose 39.1393 

Sommerville 39.1393 

Nystrom 39.1393 

Davies  and  Peck 39.13908      " 

Ganot 39.1398 

Wollaston  (1814) 39.13047      " 

Galbraith 39.139 

Byrne 39.1393 

Capt.  Kater 39.13829      " 

PARIS.— Hencke 39.12843      " 

Ganot 39.1285 

Galbraith 39.128 

Byrne 39.12843      " 

Wallace.  ..39.12843      " 


APPENDIX. 


HAVING  shown  in  the  preceding  pages  that  in  the  point 
of  view  of  scientific  accuracy  the  yard,  metre,  and  toise 
standards  are  on  a  common  level,  and  that  in  the  matter 
of  comparisons  there  is  no  extreme  accuracy,  I  will  now 
refer  to  the  proposed  change  of  our  standard  from  the 
yard  to  the  metre. 

Theoretically  the  metre  is  the  10,000,000th  part  of  the 
earth's  quadrant,  and  the  yard  the  -g^-j^VsT^  Par^  °^  a 
seconds  pendulum  at  London.  Practically,  neither  the 
metre  nor  yard  could  be  recovered  with  exactness  from 
their  natural  basis.  The  legal  French  metre  differs  from 
the  latest  reduction  enough  to  give  an  excess  of  over  three 
miles  to  the  circumference  of  the  earth.  In  fact,  the  metre- 
and  yard  are  only  the  lengths  of  bars  of  metal  kept  in 
certain  offices,  from  which  copies  are  made.  Decimally 
considered,  it  is  as  easy  to  divide  one  as  the  other  into 
tenths,  hundredths,  etc.,  and  the  yard  standard  is  often  so 
divided. 

As  to  nomenclature,  the  metrical  system  is  over- 
loaded with  Greek  arid  Latin  prefixes,  which  are  in  no 
way  so  easy  and  convenient  in  expression  as  the  short, 
sharp  Anglo-Saxon  words  yard,  foot,  inch. 

In  all  sciences  Latin  and  Greek  names  are  given  for 
easier  purposes  of  classification  ;  but  the  different  peoples 
invariably  keep  their  own  household  names  for  daily 
purposes,  leaving  prefix  and  affix  to  specialists,  probably 
with  advantage  to  both  parties. 

The  units  used  for  different  purposes  are  entirely  dis- 


23 

tinct  from  the  base  of  any  system,  and  though  always  re- 
ferable to  such  base,  are  not  practically  so  referred.  It 
therefore  seems  useless  to  burden  the  people  with  long 
scientific  names  in  the  ordinary  transactions  of  daily  life. 

For  long  distances  the  units  in  the  yard  and  metrical 
systems  are  respectively  the  mile  and  the  kilometre. 

The  mile  has  a  definite  meaning  in  our  minds,  being 
associated,  from  the  days  of  youth,  with  the  measured  dis- 
tances in  race-courses,  speed  in  walking,  railway  and 
steamer  travel,  length  of  surveyed  lots — the  same  being  in 
use  among  about  100,000,000  people. 

For  mechanical  structures,  the  units  are  respectively  the 
foot  and  the  metre.  The  foot  is  used  instead  of  the  yard, 
as  being  the  most  convenient  in  practice,  and  is  fixed  in 
the  minds  of  the  people  by  constant  association  with 
length  of  foot-rules,  size  of  buildings,  doors,  windows, 
etc.,  all  of  which  are  always  before  us. 

For  commercial  purposes  the  units  are  respectively  the 
yard  and  the  metre.  The  yard  is  associated  with  length 
of  yard-sticks,  distance  between  brass  nails  on  counters, 
so  many  finger-lengths  by  ladies.  Probably  three  fourths 
of  the  business  of  the  world  is  conducted  on  the  yard 
standard. 

For  machine  and  shop  work  the  English  unit  is  the 
inch  and  fractions,  and  countries  having  the  metrical 
standard  have  universally  adopted  the  millimetre. 

The  inch  is  well  fixed  in  the  minds  of  all  mechanics 
by  constant  use,  and  the  ease  with  which  the  fractions  are 
had  by  halving  only  renders  the  system  very  convenient. 

As  more  figures  must  be  used  to  indicate  a  size  by 
millimetres  than  by  inches  and  fractions,  it  appears  that 
the  metrical  system  cannot  shorten  the  work  of  arithmeti- 
cal computation  in  shop  work,  and  is  therefore  of  no  ad- 
vantage to  the  mechanic  or  draftsman,  but  rather  the 


reverse.  This  is  the  opinion  of  Coleman  Sellers,  the  dis- 
tinguished Philadelphia  engineer  and  manufacturer,  who, 
after  a  trial  of  the  millimetre  in  his  shops  for  some  years, 
returned  to  the  use  of  the  inch,  and  writes  in  Engineering 
News  :  "  The  loss  from  the  use  of  a  small  unit  requiring 
many  figures  to  express  what  is  needed,  takes  away  from 
the  other  advantages  of  the  system  when  considered  from 
a  labor-saving  point  of  view." 

In  France  itself  the  metrical  system  is  not  wholly  deci- 
mal in  actual  practice,  as  we  find  the  following  measures 
in  use  in  addition  to  the  decimal  divisions  :  double  deca- 
metre, de mi-decametre,  double  metre,  demi-metre,  and 
double  decimetre. 

The  metrical  system  has  been  adopted  in  the  following 
countries:  France  and  colonies,  Holland  and  colonies, 
Belgium,  Spain  and  colonies,  Portugal,  Italy,  Germany, 
Greece,  Roumania,  British  India,  Mexico,  New  Granada, 
Ecuador,  Peru,  Brazil,  Uruguay,  Argentine  Confederacy, 
Chili,  Venezuela ;  and  partially  in  Wurternburg,  Bavaria, 
Baden,  Hesse,  Switzerland,  Denmark,  Austria,  and  Turkey. 

In  the  past  centuries  all  the  work  and  records  of  Eng- 
lish-speaking peoples — now  numbering  about  100,000,000, 
and  increasing  and  progressing  faster  than  all  other 
nationalities,  as  well  as  being  closely  connected  by  de- 
scent and  business — have  been  done  and  recorded  under 
the  yard  standard,  and  any  change  now  would  inevitably 
render  necessary  continual  reductions,  to  the  great  detri- 
ment and  inconvenience  of  the  mass  of  our  people,  and 
with  little  or  no  practical  benefit,  except  perhaps  to  a  small 
class  of  scientific  and  pseudo-scientific  men,  who  can  and  do 
amuse  themselves  with  the  fancied  uniformity  of  the  metre. 

All  our  numerous  text-books  and  tables,  mechanical 
and  scientific,  would  be  rendered  entirely  useless  by  the 
change,  and  this  is  a  serious  final  consideration. 


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